It depends what you mean. In most cases the use is "in the plane" because the point is actually a part of the plane (an element in the set that we call 'plane', to be precise) instead of merely being on it. I hope this explains the difference.
Completely offtopic now:P : Oh, cool, what kind of games do you program? I once coded a game of hangman in C, and I'm trying to learn Java (mostly because I don't have windows but I want to share the programs I create), is there a book you'd recommend (especifically I'm trying to understand events: listeners and all that)?
Yes, the proof is for the n-dimensional case. The drawings are still of a loop in (on?) the plane, though:P. But yeah, your idea of 3d loop is what the author uses (in the book it's called a 'hypersurface' and it shows that it's actually the boundary of a compact manifold, and there are two connected components: 'inside' and 'outside' the hypersurface).
Well, they can use conjectures, but the "result" is often preceded by "If P is true, then the result is true, however...". The thing is that sometimes the "result" appears to be valid in many situations thus making the conjecture on which it depends appear more likely to be true (I mean that it can be proven using the other 'standard' axioms, rather than taking the conjecture as an axiom in general).
And perhaps you mean the Jordan curve Theorem? Yeah, that bastard is really intuitive but the proof is kinda hard. May I suggest -if you are interested- reading Guillemin's Differential Topology, there is a "proof" of a general version of the theorem (more like a series of exercises to prove the theorem). Very accessible book, if one is willing to believe many things without actually checking their proofs thoroughly.
Heh, and that's the thing, isn't it? Trying to abstract real world situations into some conditions for a given program to satisfy can be very challenging; for example you have to meet some presentation guidelines and what not. For academic purposes maybe it's not so complicated (it's not in many cases:P), but other applications are hard to work with.
But yeah, I think that if some situation (real world or not) can be abstracted enough for analysis using a computer, then creating a set of axioms should be not so difficult.
Sorry to be kinda pedantic, but if we are talking about an advanced math class then I wouldn't call using the epsilon delta criteria needlessly muddifying the lecture. Things should be properly justified. (Of course the intuitive explanation is very useful).
Well, yes. That's actually a tautology: math doesn't explain the world (it doesn't even try), and science is about explaining the world (although, similarly to your affirmation, I could say that physics doesn't explain the world, either, is just a language that we use to describe it -- but that's just semantics, and I see what you mean).
But, given the organization of the mathematical knowledge, I really consider it as a science. Because for me science is not just about explaining the world, I think of it more like "institutionalized knowledge", not restricted to "where the scientific method is used". This definition encompasses what you consider as sciences and more. It's completely artificial, yes, but it has its advantages when you are trying to classify some body of knowledge. 'The science of dancing' would be all the theories, observations, techniques, etc. about dancing.
This last one is mostly a joke, but I hope explains what I mean.
I was going to say "Marx: it has the x already!", but it should be a Russian name. Not that 'OS' is very Russian... and not that Marx is the same as Lenin... or Linux, for that matter:P
I can also highly recommend this book to everyone here at slashdot. It's the kind of book most of us will be able to relate to. A book by a geek who understands not only technology, but also the social implications thereof.
Slashdot Mirror
Oh, man! I loved GORILLA.BAS (I mean the game, the code I didn't understand when I was five :P).
I liked Nibbles too, but there was this level I just couldn't beat. It has two diagonal lines, I remember. Damn walls!
Hmm I guess I'm starting to get it.. ;)
That's what she said!
Oh, wait...
Inconceivable!
It depends what you mean. In most cases the use is "in the plane" because the point is actually a part of the plane (an element in the set that we call 'plane', to be precise) instead of merely being on it. I hope this explains the difference.
Completely offtopic now :P :
Oh, cool, what kind of games do you program? I once coded a game of hangman in C, and I'm trying to learn Java (mostly because I don't have windows but I want to share the programs I create), is there a book you'd recommend (especifically I'm trying to understand events: listeners and all that)?
Yes, the proof is for the n-dimensional case. The drawings are still of a loop in (on?) the plane, though :P. But yeah, your idea of 3d loop is what the author uses (in the book it's called a 'hypersurface' and it shows that it's actually the boundary of a compact manifold, and there are two connected components: 'inside' and 'outside' the hypersurface).
Well, they can use conjectures, but the "result" is often preceded by "If P is true, then the result is true, however...". The thing is that sometimes the "result" appears to be valid in many situations thus making the conjecture on which it depends appear more likely to be true (I mean that it can be proven using the other 'standard' axioms, rather than taking the conjecture as an axiom in general).
And perhaps you mean the Jordan curve Theorem? Yeah, that bastard is really intuitive but the proof is kinda hard. May I suggest -if you are interested- reading Guillemin's Differential Topology, there is a "proof" of a general version of the theorem (more like a series of exercises to prove the theorem). Very accessible book, if one is willing to believe many things without actually checking their proofs thoroughly.
Heh, and that's the thing, isn't it? Trying to abstract real world situations into some conditions for a given program to satisfy can be very challenging; for example you have to meet some presentation guidelines and what not. For academic purposes maybe it's not so complicated (it's not in many cases :P), but other applications are hard to work with.
But yeah, I think that if some situation (real world or not) can be abstracted enough for analysis using a computer, then creating a set of axioms should be not so difficult.
Now the proof, that's another thing...
Well, you can give a proof that your program "works", but that's still far from "works correctly" :P.
Your ideas are intriguing to me and I wish to subscribe to your newsletter.
Reminds me of that comment when someone wrote "*Shakes little fist*" and then Little fist replied with "cut it out". Very surreal stuff, heh.
Where 'firstname' and 'lastname' are my actual names.
Damn! Some nasty name you got there! Perhaps I'll name my son 'firstname' too!
Sorry to be kinda pedantic, but if we are talking about an advanced math class then I wouldn't call using the epsilon delta criteria needlessly muddifying the lecture. Things should be properly justified. (Of course the intuitive explanation is very useful).
Best reply I've ever seen!
Well, I was able to 'play' it at 640x480 with a Pentium 4 2.6Ghz, 768MB RAM and a geforce mx 440. It was actually enjoyable, I think.
Stupid filter is not in charge of Gundam. 'Nuff said.
It's always better than "All your worlds are belong to us".
You must be Gundam here.
You people always thinking about your booting times! Won't someone THINK OF THE CHILDREN!!?
Well, yes. That's actually a tautology: math doesn't explain the world (it doesn't even try), and science is about explaining the world (although, similarly to your affirmation, I could say that physics doesn't explain the world, either, is just a language that we use to describe it -- but that's just semantics, and I see what you mean).
But, given the organization of the mathematical knowledge, I really consider it as a science. Because for me science is not just about explaining the world, I think of it more like "institutionalized knowledge", not restricted to "where the scientific method is used". This definition encompasses what you consider as sciences and more. It's completely artificial, yes, but it has its advantages when you are trying to classify some body of knowledge. 'The science of dancing' would be all the theories, observations, techniques, etc. about dancing.
This last one is mostly a joke, but I hope explains what I mean.
I was going to say "Marx: it has the x already!", but it should be a Russian name. Not that 'OS' is very Russian... and not that Marx is the same as Lenin... or Linux, for that matter :P
You can own it, all right. Just not only you :P
More like Windows Meh :P
I need some sleep.
Yeah, man! You don't want it to be called the Windows Image Manipulation Program or something, now do you!?
You must be new here.
Brings a whole new meaning to 'going ape', no?